Modern electronic circuitry can be manufactured in several different forms, e.g. printed circuit boards (PCB's), semiconductor integrated circuits (IC's), and packaging technologies such as ball grid arrays (BGA's). All of these manufacturing technologies produce structures that are stacks of several layers. Packages and PCBs start with an insulating core layer and then add alternating layers of metal and insulator above and below the core layer. IC's start with a semiconductor substrate or “die” and add layers of insulator and metal to the top of the substrate. The metal layers are used to distribute electrical power and ground supplies to the active circuitry, or to connect analog and digital electrical signals from one circuit device to another. The insulating layers prevent unintended electrical connections from forming between neighboring metal layers. These insulating layers may all be the same material, or could be different materials or even air.
Metal layers are often dedicated entirely to a specific purpose: for example distributing power and ground supplies, or for routing electrical signals. Layers used for distributing power and ground supplies are often referred to as metal planes or conducting planes. They are almost entirely covered in metal, except for gaps needed to separate different supply voltages, and small “anti-pad” holes described below. Layers used for routing signals generally have much less metal coverage. The metallization here is typically in the form of narrow “traces” or transmission lines.
In order to provide connectivity between pathways or components on two different layers, a via can be used. A via is a conductor that connects at least two different metal layers. Vias can be manufactured by making a hole in one or more insulating layers and then completely or partially filling the hole with metal. Often the resulting via will be cylindrical in form. The upper and lower layers that a via connects can be but are not necessarily the topmost and the lowermost metal layers in the layer stack described above. Also, the upper and lower layers can be a pair of adjacent conductive layers, or there can be one or more intervening conductive layers. More than one via can facilitate electrical communication between a particular pair of upper and lower conductive layers.
In general, a via simply passes through the intervening layers, and is not physically connected to any pathway or circuit component in such intervening layers. To this end, a via passes through an opening in an intervening layer without physically contacting the layer. Therefore, a gap is present between an outer surface of the via at or near the plane of the intervening layer and an inner edge of the opening. At or near the plane of the intervening layer, within the gap, the barrel of the via may be surrounded by a portion coupled thereto called a pad. For such vias, a gap is present in or near the plane of the intervening layer between an outer edge of the pad and the inner edge of the opening through which the via passes.
In general, vias are ubiquitous components on printed circuit boards and electronic packages and are responsible for routing signals and for distributing power. Individually analyzing electrical properties of hundreds or thousands of vias using full-wave numerical methods can be computationally prohibitive. As such, in order to facilitate analysis or simulation of the circuitry, equivalent circuit models of vias can be created, and the values of the circuit elements in the models can be extracted using analytic methods. Such via models can be integrated with models of other objects, such as conductive layers or planes, transmission lines, passive/active components, etc., to form a circuit network to represent the PCB/packages or a portion thereof. Parameters of engineering significance of the PCB/packages can be also extracted.